Abstract: The measurement of a large like-sign dimuon asymmetry A(SL)(b) by the D0 experiment at the Tevatron departs noticeably from Standard Model (SM) expectations and it may be interpreted as a hint of physics beyond the Standard Model contributing to Delta B not equal 0 transitions. In this work we analyze how the natural suppression of A(SL)(b) in the SM can be circumvented by new physics. We consider generic Standard Model extensions where the charged current mixing matrix is enlarged with respect to the usual 3 x 3 unitary Cabibbo-Kobayashi-Maskawa matrix, and show how, within this framework, a significant enhancement over Standard Model expectations for Ab SL is easily reachable through enhancements of the semileptonic asymmetries A(SL)(d) and A(SL)(s) of both B-d(0)- (B) over bar (0)(d) and B-s(0)- (B) over bar (0)(s) systems. Despite being insufficient to reproduce the D0 measurement, such deviations from SM expectations may be probed by the LHCb experiment.